Deleting your gmail account and deleting your Google account are two different processes.
To delete your gmail account:
- Sign in to the Account preferences page.
- Click Delete products. You may need to sign in to your account again.
- Next to Gmail, click Delete.
- Follow the instructions on the screen, then choose Remove Gmail.
Note: If you use Gmail offline, you also need to clear your browser's cache and cookies to remove Gmail completely.
Source: Canceling your Gmail address
To delete your Google account:
- Sign in to My Account.
- Under "Account preferences," select Delete your account or services.
- Choose a service to delete or select Delete Google Account and data.
- Review what you're deleting and follow the instructions.
- Choose Delete.
Note: If you can't follow these steps, your account might have been created by your organization or company. For help, contact your admin.
Source: Delete your Google Account